Self-calibration of radio astronomical arrays with non-diagonal noise covariance matrix

The radio astronomy community is currently building a number of phased array telescopes. The calibration of these telescopes is hampered by the fact that covariances of signals from closely spaced antennas are sensitive to noise coupling and to variations in sky brightness on large spatial scales. These effects are difficult and computationally expensive to model. We propose to model them phenomenologically using a non-diagonal noise covariance matrix. The parameters can be estimated using a weighted alternating least squares (WALS) algorithm iterating between the calibration parameters and the additive nuisance parameters. We demonstrate the effectiveness of our method using data from the low frequency array (LOFAR) prototype station.